Oral presentations and abstracts
Session assets
Overview. Terrestrial planets grew in a complex series of late stage giant impacts, and Moon-formation was among last to occur around Earth. But was it a singular event? Here we propose it was three or more episodes involving two bodies and the Sun, an almost-merger followed by an interlude, followed by a merger.
The standard model originated in the 1970s and has been surprisingly resilient [1]. It succeeds at making a Moon-size moon with Moon-like rocky and volatile-depleted composition, and sets the stage for the lunar magma ocean and tidal evolution. The model is only relevant to vimp no faster than ~1.1 vesc[2], which represents the median velocity of late-stage collisions [3,4]. Larger-velocity collisions encompass the other half of the probability distribution. At one end of the energetic spectrum, Theia could have originated from further out, as proposed by [5], but these collisions are dynamically disfavored [6].
To study giant impacts outside the limited realm of efficient mergers, our group has applied machine learning [7] and physical scaling [4] to hundreds of high resolution simulations over the expected velocities and impact angles and mass ratios. A definitive conclusion is that hit-and-run collisions (HRCs) are much more probable than mergers in the common velocity range vimp ~1.1−1.4 vesc. They spin up the target, strip mantle from the projectile [8], and send it back into space along with its remnants − but do not create the Moon (although see [9]).
The solution we propose (Figure 1) is that Theia is the "runner" from a prior HRC with protoearth. The one-two blow leads to greater mixing and slows the bodies down by tens of percent so they will merge eventually. [10] found that many or even most late stage accretions are collision chains of varying complexity; on this basis we explore a three-act origin of the Moon: an HRC between prototheia and protoearth; a ~103 to 106 yr interlude featuring sweep-ups and close encounters; and a low-velocity merger resembling the standard model.
The standard model is appealing for astrophysical and petrological reasons. It invokes what seems to be a typical "late stage" accretion of two terrestrial embryos, resulting in an Earth-Moon system of the right mass and angular momentum. And it predicts a volatile-depleted silicate Moon with a small iron core. Also, it is a near-perfect merger of the type that is implicitly assumed in N-body simulations. Under those assumptions runners cannot exist.
To address the major deficiencies of the standard model while preserving its major strengths, we have developed a theoretical basis for a collision chain origin of the Moon. We show it to be a common pathway of planet formation, slowing the random velocities until merger is probable. There are innumerable pathways so it is premature to hone in on one scenario. A scenario meriting further research is an ~0.2 MEarth planet that become a mantle-stripped Theia, that then returns thousands to millions of years later for a merger on a strongly unaligned impact axis.
Modeling. Act I assumes a non-rotating protoearth 0.9 MEarth in circular orbit at 1 AU, of 30/70wt% iron/rock composition. Prototheia is 0.15 MEarth with the same composition and entropy profile. We model representative HRCs with vimp = 1.1 or 1.2 vesc and impact angles θimp = 43° to 55°. These are selected so the runner ends up ~0.1 MEarth to match the standard model. The target neither gains nor loses much mass, but it acquires a rotation period of 8 to 11 hours for these HRCs. No significant disk is produced.
We calculate the egress velocity of the runner, which we then transfer into an N-body code [11] for Act II. To represent all possible collisions, we clone each SPH outcome into 1000 random orientations and evolve each clone, including the other major planets, until they have another collision with a planet, or for 50 Myr when most giant impact chains are finished. One set of outcomes is shown in Figure 2, where the HRC velocity vimp/vesc = 1.20 (red dashed line) gets slowed down to an egress velocity of 1.01 vesc (black dashed line). Most clones return, tallied in Figure 2 by return velocity and interlude duration. Most return in ~105 years at close to the egress velocity.
By design, Act III resembles the standard model, but with an extra stage of mixing that helps solve the lunar isotope problem and slows the bodies down so that merger is probable. We apply the same compositional and entropy profiles to the target, but give it more mass (0.95 MEarth) and induce a rotation period of 8-12 hours per Act I. Theia, the runner, is now 0.1 MEarth. Some of its mantle comes from protoearth, which would further reconcile the isotopic similarities. Altough every HRC is different, for simplicity we assume one 30/70wt% runner. We set the return velocity as either 1.00 or 1.05 vesc and assume a nominal impact angle of 45°. Another variable is the offset angle between the two collisions, ranging from prograde (0°) to retrograde (180°), which would follow a random distribution [12]. The modeled return collisions are therefore variants of the standard model, and end up with a lunar mass or more in orbit in our simulations.
References
[1] Hartmann, W.K. RSPTA, 372, 20130249 (2014)
[2] Canup, R.M., Asphaug, E. Nature, 412, 708 (2001)
[3] Chambers, J.E. Icarus, 224, 43 (2013)
[4] Gabriel, T.S.J et al. ApJ, 892, 40 (2020)
[5] Budde, G. et al. Nature Astronomy, 3, 736 (2019)
[6] Jackson, A.P. et al. MNRAS, 474, 2924 (2018)
[7] Cambioni, S. et al. ApJ, 875, 40 (2019)
[8] Asphaug, E. et al. Nature, 439, 155 (2006)
[9] Reufer A. et al. Icarus, 221, 296 (2012)
[10] Emsenhuber, A. et al. ApJ, 891, 6 (2020)
[11] Chambers, J.E. MNRAS, 304, 564 (1999)
[12] Emsenhuber, A. & Asphaug, E. ApJ, 875, 95 (2019)
How to cite: Asphaug, E., Emsenhuber, A., Cambioni, S., Gabriel, T. S. J., and Schwartz, S. R.: Moon Formation in Three Acts, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-485, https://doi.org/10.5194/epsc2020-485, 2020.
Summary: Inefficient accretion is a common outcome of planet-planet collisions which dominate the late stage of terrestrial planet formation [1]. These giants impacts create deep magma oceans on the resulting bodies [2], thus promoting multi-step core formation [3]. Here we present how planetary differentiation is affected by inefficient accretion and compare the results to those obtained assuming that collisions are perfectly accretionary (“perfect merging”). We find that the two models provide similar predictions for the mass and core mass fraction of planets more massive than 0.1 Earth’s masses (~1 Mars’ mass), in agreement with previous studies [4]. At smaller scales, however, the inefficient accretion model predicts a higher degree of planetary diversity in terms of core mass fraction. Smaller final planets, by definition, do not participate in many merging giant impacts but may participate in multiple hit and run collisions as either the target or the runner, both of which may leave a strong signal in a small planet's composition. Alternatively, due to the more extensive growth history of larger final planets, these regress to an average composition through the incorporation of many smaller embryos, effectively erasing gross signatures of hit and run collisions.
Why we need to model inefficient accretion: Planet formation models typically assume that, when a target of mass MT accrete a projectile of mass MP, the resulting planet has mass MT + MP (e.g., [5]). However, numerous studies show that the projectile often manages to escape accretion (hit-and-run collisions, [6]) and substantial debris can be produced (e.g., [7, 8, 9]). We capture this effect using machine learning [10, 11]. We train neural networks to predict the outcome of the collision (mass of the resulting bodies, their post-impact orbits and core-mass-fractions) from knowledge of the impact properties (target’s and projectile’s masses, and impact angle and velocity). The training, validation and testing set is a large but sparse collection of high-resolution Smoothed Particle Hydrodynamics simulations of giant impacts. We combine the neural networks with rigorous planetary differentiation models ([12, 4]) to study how the chemical equilibrium between the Si- and Fe-rich liquids (the planets’ mantle and the core, respectively) evolve as the pressure, temperature and oxygen fugacity of metal silicate equilibration change because of a giant impact. We assume that every collision is energetic enough to re-equilibrate the planets’ reservoirs. Future work will aim to relax this assumption.
Inefficient accretion versus perfect merging: We first present a case study of a single collision solved using the inefficient accretion model trained on impact simulation data (Figure 1). Where the perfect accretion model would feature a single regime, i.e., the two bodies are assumed to merge in all scenarios, impact simulation results exhibit a richer range of potential outcomes as a function of expected pre-impact conditions. As terrestrial planets conclude their formation in a series of giant impacts [1], we also study the cumulative effect of such collision chains on the final planets' core mass fraction (Figure 2) using some of the results of the N-body planet formation studies in [11]. These simulations start with the same initial conditions, but in half of them collisions are resolved as perfect merging, while in the other half collisions are modelled using the neural networks. We find that the final planets’ core mass fractions predicted by the inefficient accretion model (dots) agree with those of the perfect merging model (diamonds) for planets’ masses larger than 0.1 Earth masses. This is consistent with previous studies that successfully reproduced Earth’s Bulk Silicate abundances using the results from N-body with perfect merging [4]. At smaller scale, however, the diversity in core mass fraction is enhanced in case inefficient accretion is included. The “degree” of diversity is higher for planets that survived a higher number of hit-and-run collisions, thus linking the collision history of planets to their core mass fractions.
Take home message: Our findings confirm that giant impacts are powerful drivers of planetary diversity, especially for planets less than a few tenths the mass of the largest, e.g. Mars-mass planets in our solar system. A realistic treatment of planetary collisions in terrestrial planet formation is necessary to accurately track compositional evolution.
References: [1] Asphaug, E. (2010). ChEG, 70, 199-219, 2010. [2] Tonks, W. B., & Melosh, H. J. (1993). JGR: Planets, 98(E3), 5319-5333. [3] Rubie, D. C., and S.A. Jacobson (2016). Deep Earth, 217:181-190. [4] Rubie, D. C. et al. (2016) Science 353.6304: 1141-1144. [5] Chambers (2001). Icarus, 152(2), 205-224, [6] Agnor, C., & Asphaug, E. (2004), ApJL, 613, L157. [7] Kokubo, E., & Genda, H. (2010), ApJL, 714, L21; [8] Stewart, S. T., & Leinhardt, Z. M. (2012), ApJ, 751, 32. [9] Burger, C et al. (2018), Celest. Mech. Dyn. Astron., 130, 2. [10] Cambioni, S., et al (2019). ApJ, 875, 40. [11] Emsenhuber, A. et al., (2020) ApJ, 891, 6. [12] Rubie, D. C., et al. (2015). Icarus 248: 89-108.
How to cite: Cambioni, S., Jacobson, S. A., Emsenhuber, A., Asphaug, E., Rubie, D. C., Gabriel, T. S. J., Furfaro, R., and Schwartz, S. R.: The Effect of Inefficient Accretion on Planetary Differentiation, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-407, https://doi.org/10.5194/epsc2020-407, 2020.
Observations of Earth-sized exoplanets are mostly limited to information on their masses and radii. Simple mass-radius relationships have been developed for scaled-up versions of Earth or other planetary bodies such as Mercury and Ganymede, as well as for one-material spheres made of pure water(-ice), silicates, or iron. However, they do not allow a thorough investigation of composition influences and thermal state on a planet’s interior structure and properties.
As shown in Figure 1, we investigate the structure of a rocky planet shortly after formation and at later stages of thermal evolution assuming the planet is differentiated into a metal core and a rocky mantle (consisting of Earth-like minerals, but with a variable iron content).
Fig. 1: Temperature (left), pressure (centre), and density (right) profiles for two example planet masses of one and two Earth masses considering
the hot temperature scenario and assuming di erent planet iron contents. From Noack and Lasbleis, 2020.
We derived possible initial temperature profiles after the accretion and magma ocean solidification following Stixrude (2014). We then developed parameterisations for the thermodynamic properties inside the core depending on planet mass, composition, and thermal state. We provide the community with robust scaling laws for the interior structure, temperature profiles, and core- and mantle-averaged thermodynamic properties for planets composed of Earth’s main minerals but with variable compositions of iron and silicates, see Figure 2.
Fig. 2: Comparison between interior structure model data (filled circles) and predicted data from our parameterised model (black empty circles)
for different planet parameters and planet masses, with colours ranging from 0.8 (dark blue) to 2 (yellow) Earth masses. Grey circles show the
individual errors. The mean error with one standard deviation is listed for each error plot. From Noack and Lasbleis, 2020.
The interior structure profiles, an online tool and the link to the repository including all Python Jupyter notebooks, that were needed to derive the scaling laws and figures of this study, as well as an implementation of the scaling laws in Python are available on the following website: http://geodyn-chic.de/tools.
The scaling laws make it possible to investigate variations in thermodynamic properties for different interior thermal states in a multitude of applications such as deriving mass-radius scaling laws or estimating magnetic field evolution and core crystallisation for rocky exoplanets.
References
Stixrude, L. 2014, Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci., 372, 20130076
Noack, L. and Lasbleis, M. 2020, A&A, 638, A129
How to cite: Noack, L. and Lasbleis, M.: Parameterisations of interior properties of rocky planets, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-947, https://doi.org/10.5194/epsc2020-947, 2020.
Introduction
Present geochemical models of planetary core formation commonly focus on either element abundances or isotope fractionation between mantle and core. Data gathered from these two techniques can be mutually inconsistent, leading to different conclusions concerning core formation processes. An example of this is the Si content of the Earth’s core. Element partitioning data and seismological observations indicate that the Earth’s core only contains minor amounts of Si [1], whereas isotopic data suggests significant amounts of Si may be present [9].
To address this data discrepancy problem, this study combines element partitioning behaviour and isotope fractionation of Fe and Zn through metal-silicate partitioning experiments. Metal-silicate partitioning experiments at high pressure and temperature allow for the distribution of elements and their isotopes between planetary cores (metal) and mantles (silicate) to be studied under controlled conditions [e.g. 6,7, 10]. As during planetary core formation it is assumed that some form of equilibrium is reached over millions of years, the experiments should reflect this as well. Therefore, it is essential to determine the time that is required for every experiment to achieve both elemental and isotopic abundance equilibrium.
Approach
Metal-silicate partitioning experiments are performed under high pressure and temperature conditions using an end-loaded piston-cylinder press. To solely focus on the equilibration times, experiments of the same starting compositions were subjected to peak conditions of 1GPa and 1823K for a time ranging from 3 minutes up to 12 hours. The experiments consisted of a synthetic analogue of the lunar Apollo 15 Green Glass as silicate phase [3], along with a metal phase of Fe-metal doped with Zn.
Element concentrations of metal and silicate phases of every experiment were measured with an electron microprobe (EMPA) for major elements and laser ablation ICP-MS (LA-ICP-MS) for trace elements. To analyse Fe and Zn isotopic fractionation, both Zn and Fe were isolated from the metal- and silicate phases through ion-exchange chromatography. The AG-X8 resin was used for the separation of Fe, and the AG-MP-1 resin for Zn [5]. The isotopes of Fe and Zn were subsequently measured using a multi-collector ICP-MS (MC-ICP-MS) with a double spike technique. The precision of the isotope analyses is determined by measuring isotopic reference materials. The standards IRMM-014 (Fe) and ETH-ZN indicate a precision of ± 0.03‰ (2SD) for Fe isotopes and ± 0.05‰ (2SD) for Zn isotopes respectively. Additionally, rock standards such as BHVO-2, BCR-2, AGV-2 and BIR-1 that had been processed exactly like the experiments were measured during the analyses.
Results
Experimental run products typically show a good separation of a metallic phase and quenched silicate melt. Disequilibrium within experiments can cause heterogeneous spots where groups of elements are clustered. These heterogeneous spots can be seen in experiments of run times of e.g. 3 and 5 minutes (Fig. 1), whereas they are absent in experiments with longer run times (Fig. 2). Results shown in Fig. 3 confirm these observations as the measured elements from short (<10 minutes) experiments show different partitioning behaviour compared to longer experiments (>30 minutes). Therefore, concentration analyses indicate that elemental equilibrium is reached within 30 minutes.
Isotope equilibration times are significantly longer than concentration equilibration times (Fig. 4 and 5) [8]. Within the first two hours of an experiment, the fractionation factors Δ56Femetal-silicate and Δ66Znmetal-silicate are positive and variable. Between 2-4 hours, the fractionation factors become negative and start to stabilise. After approximately 4 hours, isotopic equilibrium is reached for both Fe and Zn with Δ56Femetal-silicate = -0.04‰ ± 0.07 and Δ66Znmetal-silicate = -0.11‰ ± 0.06, which corresponds with literature data [2,4].
Discussion and outlook
Although the data described here cannot be directly applied to planetary core formation models yet, it is essential for creating models of core formation based on a combination of elemental abundances and stable isotope fractionation. This initial data set suggests that there is a relatively uniform Fe and Zn distribution between core (metal) and mantle (silicate) during core formation at high temperature. However, quantification of the effects of pressure, temperature and composition will be needed to further test this hypothesis.
Acknowledgements
We would like to thank the Netherlands Space Office for financial support through its User Support Programme.
References
[1] Badro, J., Côté, AS., and Brodholt, JP.: A seismologically consistent compositional model of Earth’s core, Proceedings of the National Academy of Sciences, 11, pp. 7542-7545, 2014.
[2] Bridgestock LJ., Williams H., et al.: Unlocking the zinc isotope systematics of iron meteorites, Earth and Planetary Science Letters, 400, pp. 153-164, 2014.
[3] Delano, JW.: Pristine lunar glasses : criteria, data and implications, Journal of Geophysical Research, 91, pp. 201-213, 1986.
[4] Hin RC., Schmidt MW., Bourdon B.: Experimental evidence for the absence of iron isotope fractionation between metal and silicate liquids at 1GPa and 1250-1300°C and its cosmochemical consequences, Geochimica et Cosmochimica Acta, 93, pp. 164-181, 2012.
[5] Moeller K., Schoenberg R., et al.: Calibration of the New Certified Reference Materials ERM-AE633 and ERM-AE647 for Copper and IRMM-3702 for Zinc Isotope Amount Ratio Determinations, Geostandards and Geoanalytical Research, 36, pp. 177-199, 2012.
[6] Righter, K .: Metal-silicate partitioning of siderophile elements and core formation in the early Earth, Annual Reviews of Earth and Planetary Sciences, 31, pp 135-174, 2002.
[7] Rose-Weston, L., Brenan, JM., Fei, Y., et al .: Effect of pressure, temperature and oxygen fugacity on metal-silicate partitioning of Te, Se and S: Implications for Earth differentiation, Geochimica et Cosmochimica Acta, 73, pp.4598-4615, 2009.
[8] Roskosz, M., Luais, B., Watson, HC., et al .: Experimental quantification of the fractionation of Fe isotopes during metal segregation from a silicate melt, Earth and Planetary Science Letters, 248, pp. 851-867, 2006.
[9] Shahar, A., Ziegler, K., Young, ED., et al .: Experimentally determined Si isotope fractionation between silicate and Fe metal and implications for Earth’s core formation, Earth and Planetary Science Letters, 288, pp. 228-234, 2009.
[10] Siebert, J., Corgne, A., Ryerson, FJ .: Systematics of metal-silicate partitioning for many siderophile elements applied to Earth’s core formation, Geochimica et Cosmochimica Acta, 75, pp. 1451-1489, 2011.
How to cite: Seegers, A., van Zuilen, K., Stelwagen, R., van Westrenen, W., and Vroon, P.: Equilibration time of Fe & Zn concentrations and isotopes in metal-silicate partitioning experiments, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-824, https://doi.org/10.5194/epsc2020-824, 2020.
Overview
Tidal interaction plays a unique role in coupling the thermal, orbital, and rotational evolution of close-in moons and exoplanets. The reaction of a planetary body subjected to tidal loading is determined by its interior structure, rheological properties, and orbital parameters. The interior and orbital dynamics are, conversely, affected by the tidal dissipation. In this study, we address the parameter dependence of stable spin states and tidal heating, as well as the long-term coupled thermal-orbital evolution of rocky exoplanets. Special attention is paid to the consistent evolution of spin rate and to the role of an emerging subsurface magma ocean in the secular maintenance of nonzero orbital eccentricity.
Model and Methods
Our model consists of several modules and relies on the semi-analytical description of the thermal and orbital dynamics. All processes are interconnected through the tidal dissipation, which drains the energy from the orbit and presents an additional heat source for the planetary interior. The tidal heat rate (e.g., Segatz 1988; Efroimsky and Makarov, 2014) as well as the evolution equations for the orbital parameters and the spin rate are calculated using the Darwin-Kaula expansion into modes corresponding to different tidal frequencies (Kaula, 1964). To quantify the deformation and the additional potential of the deformed planet, we calculate the complex tidal Love numbers k2*(ω) (e.g., Castillo-Rogez et al., 2011) using the equations of the normal mode theory (e.g., Sabadini and Vermeersen, 2004). This approach permits us to account for a differentiated interior of the planet.
The thermal evolution of the model planets is described by a parametrized model of stagnant lid convection (e.g., Grott and Breuer, 2008) with basal and volumetric heating, where the major heat source is provided by the tidal dissipation. The internal dynamics are coupled to the rest of the model through the temperature dependence of mantle viscosity, the evolution of the stagnant lid thickness and the emergence of a stable subsurface magma ocean. All changes in the interior structure and rheological properties are reflected by the tidal Love number, which determines the tidal response and the rate of energy dissipation.
Results
The first goal of this study is to explore the parametric dependence of the tidal dissipation and the spin-orbit locking. We study the effect of different rheological parameters, the planet size, the interior structure, and the eccentricity. As a result of the viscoelastic rheology, the model planet can get locked into higher than synchronous spin-orbit resonances, which provide an important source of dissipation especially in the case of relatively low orbital eccentricities. We also find that planets with smaller radii are more likely to get locked into higher resonances than larger or more massive planets. In addition to a parametric study of a generic terrestrial exoplanet, we also apply the model on three currently known low-mass exoplanet candidates: Proxima Centauri b, GJ 411 b, and GJ 625 b.
The second goal is the assessment of the mutual interconnection between the secular thermal and orbital evolution. We investigate the evolution paths of the three mentioned exoplanets and observe that the thermal evolution proceeds as a sequence of thermal equilibria. The equilibrium temperature profiles of the tidally evolving exoplanets are governed primarily by the stable spin-orbit ratio, which is determined by the mantle viscosity and eccentricity. The temperature-driven changes in the interior and the transitions between different spin-orbit resonances also affect the rate of orbital evolution. Specifically, the final despinning of a planet to the synchronous rotation may slow down the circularization of the planetary orbit and help to maintain nonzero orbital eccentricity for a considerable time. Using the coupled model, we also study the effect of different initial eccentricities and mantle viscosities on the current thermal and rotational state of the three exoplanets and compare the resulting eccentricities with their current, empirically given values (Figure 1).
Figure 1: Orbital and thermal characteristics of Proxima Centauri b after 5 Gyr of coupled thermal-orbital evolution; adapted from Walterova and Behounkova (2020). Depending on the initial orbital eccentricity (x-axis) and the reference viscosity at temperature T0=1600 K (y-axis), the individual panels depict the evolved eccentricity (left), the spin-orbit ratio (middle) and the surface tidal heat flux (right). Light blue areas correspond to the model parameters for which the evolved eccentricity complies with observation (Jenkins et al., 2019). The range of the empirically given values is also indicated by a red line in the first colorbar.
Conclusion
The orbital evolution of strongly tidally loaded exoplanets, whose thermal state is shaped by the tidal heating, is naturally interconnected with their internal dynamics. The changes in the interior, namely the partial melting and the formation of a subsurface magma ocean, translate into the decrease in the rate of orbital evolution and in the tidal heat generation. The understanding of this complex feedback may help us to better constrain the conditions on extrasolar worlds and to address their hypothetical habitability.
Acknowledgements
The research leading to these results received funding from the Czech Science Foundation through project No. 19-10809S and from Charles University through project SVV 115-09/260581.
References
[1] M. Segatz, T. Spohn, M. N. Ross, and G. Schubert. Icarus, 75(2):187–206,1988.
[2] M. Efroimsky and V. V. Makarov. The Astrophysical Journal, 795(1):19, 2014.
[3] W. M. Kaula. Reviews of Geophysics, 2(4):661–685, 1964.
[4] J. C. Castillo-Rogez, M. Efroimsky, and V. Lainey. Journal of Geophysical Research, 116(E09008), 2011.
[5] R. Sabadini and B. Vermeersen. Global Dynamics of the Earth: Applications of Normal Mode Relaxation Theory to Solid-Earth Geophysics. Kluwer Academic Publishers, Dordrecht, the Netherlands, 2004.
[6] M. Grott and D. Breuer. Icarus, 193(2):503–515, 2008.
[7] M. Walterova and M. Behounkova. Submitted to The Astrophysical Journal.
[8] J. S. Jenkins, J. Harrington, R. C. Challener, et al. Monthly Notices of the Royal Astronomical Society, 487(1):268–274, 2019.
How to cite: Walterova, M. and Behounkova, M.: The long-term tidal dynamics of differentiated rocky exoplanets, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-86, https://doi.org/10.5194/epsc2020-86, 2020.
Abstract
Ultra-short period planets (USP) that are rocky in nature are plentiful in the exoplanet catalogue and may host tectonic regimes without analogues in the Solar System. Recently, the transit phase-curve of the super-Earth LHS 3844b (radius = 1.303 Earth radii) has been mapped by a 100 h Spitzer observing campaign and is consistent with a bare-rock model of a tidally-locked planet [3]. We use phase map estimates of the planet's surface temperature distribution to infer the interior dynamics of LHS 3844b using a simulation of interior flow. We infer that the strong dichotomy of surface temperature may lead to a dichotomy of interior dynamics, with implications for the interior-atmosphere exchange of volatiles in USP rocky planets. We use a mantle convection code with parameters from the literature suitable for LHS 3844b. The material properties of the interior, including viscosity, are constrained from previous theoretical calculations and laboratory experiments.
For models with a weak near-surface layer (lithosphere), hot upwellings are evenly distributed between the dayside and nightside, albeit strong cold downwellings form dominantly on the nightside. Upwellings on the nightside have less lateral mobility than the dayside because they are confined by downwellings. In contrast, for models with a strong near-surface layer (lithosphere), the interior dynamics are mostly driven by a prominent downwelling on the dayside which flushes hot material from the lower thermal boundary layer around the core towards the nightside where upwellings preferentially arise. Therefore, current and near-future space missions could detect a signal from volatile outgassing or volcanism driven by interior upwellings that is either globally uniform or originating from the nightside only. A spatially-variable release of volatiles may produce corresponding asymmetries in astrophysical observations, such as secondary features in phase curves.
1. Methods
The geodynamic model is devised assuming an Earth-like composition with Perovskite (Pv) dominating the uppermost mantle and post-Perovskite (pPv) the lowermost mantle. A temperature- and pressure-dependent Arrhenius-type viscosity law is used with the lower-bound post-Perovskite parameters given in [2]. Mantle convection is modelled using the code StagYY [3] in a two-dimensional spherical annulus geometry. The effects of compressibility are modelled by employing the truncated anelastic liquid approximation (TALA) where a reference state density profile is assumed.
We include plastic yielding to model the brittle nature of the lithosphere. Yielding occurs when the local stress state exceeds a prescribed yield stress criteria, thereby modelling plate-tectonic-like behaviour at the surface.
2. Results and Discussion
For models with a weak near-surface layer (low yield stress criteria), we find that hot upwellings are evenly distributed around the CMB. Downwellings form on both sides, but they are stronger on the nightside (Figure 1). The high viscosity upwellings tend to dictate the long-wavelength pattern of flow, and therefore shepherd the upwellings along the CMB into position between the downwellings. On the dayside, the upwellings exhibit more lateral motion as the downwellings are less viscous and thus the shepherding effect is less pronounced.
For a strong near-surface layer (large yield stress), an approximate degree-1 convection pattern is established: a prominent downwelling forms on the dayside and descends into the deep mantle. It flushes hot material from the lower thermal boundary layer around the CMB from the dayside to the nightside, thereby promoting the formation of upwellings on the nightside which rise to the surface. A return flow of cold material from the nightside to the dayside is established in the uppermost Perovskite layer (Figure 2).
An explanation for this flow pattern is that yielding does not occur on the nightside and therefore the formation of downwellings is inhibited. On the dayside, high temperatures weaken the near-surface through the strong temperature dependance of viscosity and therefore enable downwellings to form.
Previous work studying the interior dynamics of incompressible Earth-sized planets with asymmetric surface temperatures finds a flow pattern that is characterised by an upwelling near the substellar point and a near-surface flow from the dayside to the nightside [4]. Although this is also a degree-1 flow, it is reversed compared to our models. We surmise that the difference in flow direction is due to the strongly varying viscosity that we impose, and possibly the effects of compressibility and planet size.
In summary, our models show that a strong dichotomy of the surface temperature can lead to an asymmetry in the distribution of upwellings and downwellings in the interior of rocky super-Earths, depending on the strength of the near-surface layer.
An asymmetric flow pattern has not been inferred for any of the rocky Solar System planets, and therefore our work presents the first observation-constrained inference of a novel tectonic mode that is applicable to some rocky exoplanets. In this regime, upwellings could produce corresponding asymmetry in the production of near-surface melt and subsequent outgassing, which can serve as a future test to distinguish between different model predictions.
Acknowledgements
TGM and DJB acknowledge Swiss National Science Foundation (SNSF) Ambizione Grant 173992.
References
[1] Tackley, Paul J.: Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the Yin-Yang grid, Physics of the Earth and Planetary Interiors, Vol. 171, pp. 7-18, 2008.
[2] Tackley, Paul J., et al.: Mantle dynamics in super-Earths: Post-perovskite rheology and self-regulation of viscosity, Vol. 225, pp. 50-61, 2013.
[3] Kreidberg, L., et al.: Absence of a thick atmosphere on the terrestrial exoplanet LHS 3844b, Vol. 573, pp. 87-90, 2019.
[4] Van Summeren, J., Conrad, C. P. and Gaidos, E.: Mantle convection, plate tectonics, and volcanism on hot exo-earths, Vol. 736, pp. 2-7, 2011.
How to cite: Meier, T. G., Bower, D. J., Lichtenberg, T., and Tackley, P. J.: Interior dynamics of tidally locked super-Earths: The case of LHS 3844b, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-778, https://doi.org/10.5194/epsc2020-778, 2020.
Melting processes inside the mantle of terrestrial planets are highly dependent on the planet’s heat budget and trigger the redistribution of incompatible trace elements from solid mantle rocks into the melt. Due to density contrasts, convective mantle motion, and other physical factors, this melt ascents towards the surface and takes most of these incompatible elements with it. Some of these ascending elements like 40K, 232Th, and 238U, are radioactive and are important contributors to the Earth’s or other terrestrial planet’s heat budget. By redistributing these elements, the mantle is left depleted and the surface enriched, leading to a shift in the production of heat from the mantle towards the crust.
To be able to calculate the amount of redistributed heat producing elements, we model partition coefficients after Blundy and Wood 2003 [1] depending on temperature, pressure, and melt composition and trace them in a global convection code (Fig.1). For the incorporation of the elements’ partitioning behavior at higher upper mantle pressures, we took the thermodynamic approach from Blundy et al. 1995 [2] and parameterized it to higher pressures (Fig.2). The redistribution of heat producing elements between the mantle and crust has important implications for the cooling behavior of the interior. In turn, the latter affects the generation of melt in the mantle and the formation of crust.
[1] Blundy, J.D. and Wood, B.J. (2003), RiMG, 52 (1), 59–123.
[2] Blundy, J.D., Falloon, T.J., Wood, B.J., and Dalton, J.A. (1995), J. Geophys. Res., 100, 15501-15515.
Fig. 1: Redistributed amount of the heat sources 40K, 232Th, and 238U on Mars after 600 Myrs.
Fig. 2: The clinopyroxene/melt partition coefficient of Na parameterized to higher pressures. With increasing pressures, partition coefficients increase. At the turning point, the model ceases to work. The applicability of the approach could be increased from 0-4 GPa to ≤12 GPa.
How to cite: Schmidt, J. M. and Noack, L.: Mantle evolution in terrestrial planets - Partitioning behavior of heat producing elements, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-966, https://doi.org/10.5194/epsc2020-966, 2020.
